Three-point-bending and double-notch shear experiments are modeled using a continuum damage mechanics approach, and an explicit fracture mechanics approach, for both homogeneous and heterogeneous rocks. The local damage approach uses the Mazars isotropic damage model. In the explicit fracture simulations, fractures are represented as explicit surfaces within a threedimensional unstructured mesh comprised of isoparametric quadratic tetrahedra and quarter point tetrahedra. Heterogeneities in strength, stiffness and toughness are introduced in a random manner within ±50% of the average values. A characteristic length is used to define the size of element clusters having uniform properties. Both approaches are used to evaluate the influence of material heterogeneity on crack propagation and interaction. Both models reproduce well the experimental results for homogeneous rocks. While in the damage model the mesh is fixed and refined globally, the discrete approach only requires refinement around the fracture tips. In the three-point-bending and double-notch shear simulations, the damage mechanics approach is more realistic in that it leads to rougher crack surfaces. However, the fracture mechanics model predicts lower curvature of the fracture, which better corresponds to experimental observations. Both approaches predict that the presence of heterogeneities seems to diminish fracture interaction.
Various continuous and discrete numerical models have been proposed to model crack growth in homogeneous materials. However, many materials, such as concrete, rocks, and other quasi-brittle materials, contain heterogeneities, which may affect the growth of fractures (Figure 1).
Damage models, derived within the general framework of continuum damage mechanics, are often used to reproduce the effects of stiffness degradation, without explicitly representing discrete fractures. Models for quasi-brittle damage include micromechanical models, as well as isotropic and anisotropic empirical models. Micromechanical damage models are the most advanced, in that they model microscopic phenomena responsible for the evolution of damage through first-order principles (Krajcinovic, 1986). They are therefore very useful for understanding rock failure. However, they are computationally demanding to implement.